20 10 Daxing second model mathematics test questions and answers

Daxing District 2009-20 10 school year second semester simulation test paper (2)

Grade three mathematics

Instructions for candidates 1. This paper is ***6 pages, * * * 5 big questions and 25 small questions, with full marks 120. Examination time 120 minutes.

2. Fill in the school name, name and admission ticket number carefully on the test paper and answer sheet.

The answers to the questions are written on the answer sheet, and the answers on the test paper are invalid.

Please return the answer sheet and the draft paper together after the exam.

The first volume (multiple choice questions, ***32 points)

First, multiple-choice questions (32 points for this question, 4 points for each small question)

Of the four alternative answers to the following questions, only one is correct. Please write the letters in front of the correct answers on the answer sheet.

The absolute value of 1 -8 equals ()

A. 8th century BC to 8th century BC.

2. If an angle is equal to 56, then its complementary angle is equal to ()

A.24 B. 56 C. 34 D. 36

3. As shown in figure 1, it is the chord of ⊙O, in

Point, if,, then the radius of ⊙O is () cm.

A. 10

4. The following operation is correct ()

A.B.

C.D.

In order to prepare for the 20 10 Winter Olympics, Zhou Yang trained hard in the short track 1500m speed skating. In order to judge whether her performance is stable, the coach made a statistical analysis of her 10 training performance, so the coach should know the () of this 10 performance.

A. mode b variance c mean d frequency

6. If the sum of the inner angles of a polygon is equal to 2.5 times the sum of the outer angles, the number of sides of the polygon is ().

a4 b . 5 c . 6d . 7

7. As shown in Figure 2, AB is the diameter of ⊙O, points D and E are bisectors of a semicircle, and the extension lines of AE and BD intersect at point C. If CE=2, the sum of shadow areas in ⊙O is ().

A.B.

C.D.

8. As shown in Figure 3-6, a rectangular piece of paper is folded in half, the crease is AB, with the midpoint O of AB as the vertex, the flat angle ∠AOB is divided into three parts, folded along the bisector of the flat angle, and the folded figure is cut into an isosceles triangle with O as the vertex, then the cut-out plane figure must be ().

A. regular triangle B. square C. regular pentagon D. regular hexagon

Volume II (***88 points)

II. Fill in the blanks (the score for this question is *** 16, with 4 points for each small question)

9. If the score is 0, the value of a is.

10. In the function y=, the range of the independent variable x is.

The minimum value of 1 1. algebraic expression is.

12. As shown in Figure 7, in the plane rectangular coordinate system xOy, the isosceles trapezoid ABCD

The vertex coordinates of are A( 1, 1), B(2,-1), c (-2,-1),

D (- 1， 1)。 Point P (0 0,2) on the Y axis rotates around point A 180.

Get point P 1, point P 1 rotate around point b 180, and point P2 rotates around point C.

Rotate 180 to get point P3, then the coordinate of point P3 is (,).

Iii. Answer the question (30 points for this question, 5 points for each small question)

13. Calculation:.

14. Solve the equation:.

15. As we all know, as shown in Figure 8, in the parallelogram ABCD, points E and F are located respectively.

On AB and DC, AE = CF

Proof: ∠ Ade = ∠ CBF.

16. If, find the value of the algebraic expression.

17. In the plane rectangular coordinate system, the image of a linear function is symmetrical with that of a linear function and intersects with that of an inverse proportional function at a point. Try to determine the value of n.

18. As shown in Figure 9, the line segments represent the heights of buildings A and B respectively, and the elevation angle of the point measured from the point is 60, and the elevation angle of the point measured from the point is 30. It is known that the height AB of Building A is 36 meters. Find the height DC of building B.

Iv. Answer (20 points for this question, 5 points for 19, 5 points for 20 questions, 4 points for 2 1 question, and 6 points for 22 questions)

19. An automobile factory decided to recruit some new workers, and they went to work after training. The investigation department found that 1 skilled workers and two new workers can install eight electric vehicles every month, and two skilled workers and three new workers can install 14 electric vehicles every month. How many electric vehicles can each skilled worker and new worker install?

20 .. As shown in figure 10, it is a circumscribed circle, passing through the point, and the intersection extension line is at the point.

(1) Verification: the tangent of Yes;

(2) If the radius r is 5 and BC=8, find the length of the line segment.

2 1. With the popularity of the Internet, more and more people like to shop online. From 2005 to 2008, a company investigated the number of online stores and the number of shoppers on a website. According to the survey results, the number of online stores in this website in recent four years and the average number of customers in each online store are made into broken-line statistical charts (as shown in figure 1 1) and bar statistical charts (as shown in figure 12). Please fill in the following blanks according to the information provided in the statistical chart:

(1) In 2005, this website had an online shop.

(2) In 2008, the website had10,000 online shoppers.

22. Figure 13 is a rectangular piece of paper, the ratio of its Zhang Kuan to its length. We call this rectangle the golden rectangle. As you all know, if you fold according to the folding method shown in Figure 14, you can get a square ABEF and a rectangular EFDC. Is EFDC a rectangle or a golden rectangle? If yes, please prove your conclusion according to figure 14; If not, please explain why.

Five, answer (this question ***22 points, 23 questions 7 points, 24 questions 7 points, 25 questions 8 points)

23. as shown in figure 15, in Rt△ABC, ∠ C = 90, BC = 8 cm, point d is on AC, and CD = 3 cm. Point P and point Q start from point A and point C, respectively. Point P moves to point C at a constant speed in AC direction, with a speed of K cm per second, and the time to complete the whole AC journey is 8 seconds. Point Q moves to point B in CB direction at a constant speed of 1 cm per second. Let the moving time be seconds, the area of △DCQ is square centimeter, and the area of △PCQ is square centimeter.

(1) Find the function relation of sum and draw the image in figure 16;

(2) As shown in figure 16, the image is a part of a parabola, and its vertex coordinates are (4, 12). Find the speed of point P and the length of AC;

(3) In figure 16, point G is a point on the positive semi-axis of the shaft. If it passes through G, EF is perpendicular to the shaft, and the intersecting and intersecting images are at point E and point F respectively.

① Tell the practical significance of the length of line segment EF in Figure 15;

② When 0 < < 6, find the maximum length of line segment EF.

24. In the plane rectangular coordinate system, it is known that the straight line intersects the parabola at point B (0 0,4) and point C (5 5,9), and the straight line BC intersects the X axis at point A. 。

(1) Find the coordinates of point A and the parabola symmetry axis;

(2) D( 1, y) on the parabola, whether there are two points M and N on the axis of symmetry of the parabola, and MN=2, and M is above N, so that the perimeter of the quadrilateral BDNM is the smallest. If yes, find out the coordinates of m and n points; If not, please explain why.

(3) Find all points p on the parabola that satisfy the distance to the straight line BC.

25. As shown in Figure 17 and Figure 18, there are two isosceles right angles △DMN and △ABC, with similar ratios. Take these two triangles as shown in figure 19, and the hypotenuse MN of △DMN coincides with the right angle AC of △ABC.

(1) In Figure 19, rotate △DMN around this point so that two right-angled sides DM and DN intersect at this point respectively, as shown in Figure 20.

(2) In Figure 19, rotate △DMN around this point, so that the extension lines of the hypotenuse CM and the right angle edge intersect with this point respectively, as shown in Figure 2 1. Is the conclusion still valid at this time? If yes, please give proof; If not, please explain why.

(3) As shown in Figure 22, in a square, the sum of points on the sides satisfies the circumference equal to half of the circumference of the square, and the sum of points, line segments and just can form a triangle. Please point out the shape of the triangle composed of line segments and give proof.

Daxing district 2009~20 10 school year second semester simulation test paper (2)

Mathematics reference answers and grading standards for grade three.

First, multiple-choice questions (32 points for this question, 4 points for each small question)

1.A 2。 C 3。 B 4。 A 5。 B 6。 D 7。 An eight. D

Volume II (***88 points)

II. Fill in the blanks (the score for this question is *** 16, with 4 points for each small question)

9.2 10. 1 1. 12.(-6,0)

Iii. Answer the question (30 points for this question, 5 points for each small question)

=10.5 points.

14. Solution: Remove the denominator.

............................................, two points.

Solution ... 4 o'clock.

Proved to be the solution of the original equation.

So the solution of the original equation is

15. It is proved that the ∵ quadrilateral ABCD is a parallelogram.

∴ ad = CB, ................................................................................................. 1 min.

∠ A = ∠ C。 .........................................................................................., two points.

In AED delta and CFB delta,

∴△ AED△ CFB ............................................................................................... 4 points.

∴∠ Adebayor = ∠ CBF .............................................................. 5 points.

16. Solution:

.........................................., two points.

Three points

Four points.

By, by

The original formula is 5 points.

17. According to the question,

The analytical formula of linear function is

Because the point A(m, 3) is on the image of the linear function,

So ... three points.

That is, the coordinate of point A is (-3,3).

Point A (-3,3) is in

Five points.

18. Solution: (1) The passing point is done at the point.

Two points.

Settings, and then,

Yes,

x，

.3 points

Yes,

Iv. Answer (20 points for this question, 5 points for 19, 5 points for 20 questions, 4 points for 2 1 question, and 6 points for 22 questions)

19. Solution: (1) Assume that every skilled worker and new worker can install an electric car. .....................................................................................................................................

Three points

The solution is 4 o'clock.

Answer: Each skilled worker and new worker can install 4 and 2 electric vehicles every month. ......................................... scored 5 points respectively.

20. Solution: (1) Proof:

∴∠ADB=90

∴∠ADB=∠PAD=90。

∴AO⊥AP

∫AO is the radius,

........................ scored 2 points as the tangent of.

(2)∵AO⊥BC, BC =8

∴BD=DC=4.

At Rt△BDO,

OB = 5，

∴ ...................................................... 3 points.

∠∠BDO =∠OAP = 90。

∠AOP=∠BOD

∴△AOP∽△DOB 4 points

Namely.

Five points.

2 1.( 1) 20 2 points.

(2) 4 points for 3600 ...........................................................

20. Solution: The rectangular EFDC is a golden rectangle ..................................................... 1 min.

Prove that the quadrilateral ABEF is a square.

Ab = dc = af points.

It's also VIII

∴

That is, point F is the golden section of line segment AD. .................................................................................................................................................................

∴4 points

Five points.

∴ Rectangular CDFE is a golden rectangle with 6 points.

Five, answer (this question ***22 points, 23 questions 7 points, 24 questions 7 points, 25 questions 8 points)

23. solution: (1) ∵, CD = 3, CQ = X.

∴ ...................................1min.

As shown in figure 16, the image is 2 points.

⑵、CP=8k-xk，CQ=x，

∴.. 3 points

∫ Parabolic vertex coordinates are (4 12),

I see.

Then the speed of point P is centimeters per second, and AC =12cm. ....................................................................................................................................................

(3) (1) observe the image and know.

The length of the line segment represents the area difference between △PCQ and △DCQ (or the area of △PDQ) ... 5 points.

② From (1) to (2).

∫EF = y2-y 1，

∴ ef = .............................................. 6 points.

The coefficient of ∫ quadratic term is less than 0, 0 < x < 6,

∴ At an appropriate time, the maximum is ............................................. 7 points.

24. Solution: (1)

The symmetry axis of parabola is: straight line ............................................ 1 min.

(2) If the perimeter of a quadrilateral is the shortest, find the shortest.

On the parabola at point d,

∴ D( 1， 1)

∴ The symmetrical point of point D about a straight line is

∫B(0，4)

∴ Translate point B downward by 2 units to get (0,2).

∴ A straight line intersects a straight line at point n,

∵ (0,2),

∴ The analytical formula of straight line is: straight line.

∴N

MN = 2

∴3 points

(3) The distance from point P to BC line is H, so point P should be on the sum of upper and lower parallel lines parallel to BC line and separated from each other. ......................................................................................................................................

According to the nature of parallel lines, the distance from the intersection of two parallel lines and Y axis to BC line is also.

As shown in the figure, let it intersect with the Y axis at point E, and pass through EF⊥BC at point F.

In Rt△BEF,

∴

You can get the coordinates of the intersection of the straight line and the Y axis as follows

Similarly, the coordinates of the intersection of a straight line and the Y axis can be obtained by the following formula

∴ analytical formula of two straight lines; .

List the equation according to the meaning of the question: (1);

(2) 6 points.

∴ Solving: ;

There are four points P that meet the requirements. They are,,, ... with 7 points respectively.

25.( 1) proof: as shown in figure 20, extend ED to E', make ED = DE', and connect e' b.